Angular Dispersion Assignment Help

Angular Dispersion

Angular dispersion produced by a prism for white light is the difference in the angles of deviation of two extreme colors i.e. violet and red colors. In others, it is the angle in which all colors of white light are contained, fig. 1.

If δv = deviation of violet color

δr = deviation of red color

Then, angular dispersion = δv – δr

Now, the deviation δ through a thin prism of refracting angle A is

δ = (µ - 1) A

Therefore, δv = (µv – 1) A (1)

And δr = (µr – 1) A (2)

Subtracting, (2) from (1), we get

δv – δr = (µv – 1)A - (µr – 1)A

= (µv – 1 - µr + 1) A

Therefore, angular dispersion,

(δv – δr) = (µv - µr) A (3)

Obviously, angular dispersion produced by a prism depends upon (i) angle of prism, (ii) nature of material of the prism.

Dispersion power

The dispersion power of a prism is defined as the ratio of angular dispersion to the mean deviation produced by the prism. It is represented by ω.